How to configure nginx so it works with Express?

You express configured to serve path /index.html, but you requires /test-express/index.html. Either configure express to serve /test-express/index.html or make nginx to strip /test-exress from proxied request. Latter is as simple as add trailing slashes to location and proxy_pass.

location /test-express/ {
  proxy_pass    http://127.0.0.1:3002/;
}

See http://nginx.org/r/proxy_pass for details.